Problem: What do the following two equations represent? $5x-2y = -5$ $8x+20y = -2$
Solution: Putting the first equation in $y = mx + b$ form gives: $5x-2y = -5$ $-2y = -5x-5$ $y = \dfrac{5}{2}x + \dfrac{5}{2}$ Putting the second equation in $y = mx + b$ form gives: $8x+20y = -2$ $20y = -8x-2$ $y = -\dfrac{2}{5}x - \dfrac{1}{10}$ The slopes are negative inverses of each other, so the lines are perpendicular.